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A pre-stack migration algorithm for elastic waves in two-dimensional variable-velocity media is developed, implemented, and tested. The algorithm operates in the time-space domain and is based on reverse-time finite-difference extrapolation of elastic waves. The algorithm is explained and demonstrated in the context of imaging of elastic vertical seismic profile data, but is applicable to any source-recorder geometry. Synthetic test examples include a point diffractor, laterally homogeneous layers, and the flank of a salt dome.